%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:05:32 PM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 12 unt; 8 def)
% Number of atoms : 209 ( 67 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 252 ( 108 ~; 103 |; 25 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 27 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X2
| app(X5,cons(X4,nil)) != X3 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X0
& app(X7,cons(X6,nil)) = X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X2
| app(X5,cons(X4,nil)) != X3 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X0
& app(X7,cons(X6,nil)) = X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X2
& app(X5,cons(X4,nil)) = X3 )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X0
| app(X7,cons(X6,nil)) != X1 ) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f410,plain,
! [X6,X7] :
( app(X7,cons(X6,nil)) != sK48
| app(cons(X6,nil),X7) != sK47
| ~ ssList(X7)
| ~ ssItem(X6)
| nil != sK47 ),
inference(cnf_transformation,[],[f221]) ).
fof(f411,plain,
! [X6,X7] :
( app(X7,cons(X6,nil)) != sK48
| app(cons(X6,nil),X7) != sK47
| ~ ssList(X7)
| ~ ssItem(X6)
| nil = sK48 ),
inference(cnf_transformation,[],[f221]) ).
fof(f412,plain,
( ~ neq(sK50,nil)
| sK50 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f413,plain,
( ~ neq(sK50,nil)
| sK49 = app(cons(sK51,nil),sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
( neq(sK48,nil)
| nil != sK47 ),
inference(cnf_transformation,[],[f221]) ).
fof(f417,plain,
( neq(sK48,nil)
| nil = sK48 ),
inference(cnf_transformation,[],[f221]) ).
fof(f418,plain,
( nil != sK50
| nil = sK49 ),
inference(cnf_transformation,[],[f221]) ).
fof(f419,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f420,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f221]) ).
fof(f427,plain,
( neq(sK50,nil)
| nil = sK50 ),
inference(definition_unfolding,[],[f417,f420,f420]) ).
fof(f428,plain,
( neq(sK50,nil)
| nil != sK49 ),
inference(definition_unfolding,[],[f416,f420,f419]) ).
fof(f429,plain,
! [X6,X7] :
( app(X7,cons(X6,nil)) != sK50
| app(cons(X6,nil),X7) != sK49
| ~ ssList(X7)
| ~ ssItem(X6)
| nil = sK50 ),
inference(definition_unfolding,[],[f411,f420,f419,f420]) ).
fof(f430,plain,
! [X6,X7] :
( app(X7,cons(X6,nil)) != sK50
| app(cons(X6,nil),X7) != sK49
| ~ ssList(X7)
| ~ ssItem(X6)
| nil != sK49 ),
inference(definition_unfolding,[],[f410,f420,f419,f419]) ).
fof(f464,definition,
( spl53_1
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f468,definition,
( spl53_2
<=> ! [X6,X7] :
( app(X7,cons(X6,nil)) != sK50
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK49 ) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f469,plain,
( ! [X6,X7] :
( ~ ssItem(X6)
| app(X7,cons(X6,nil)) != sK50
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK49 )
| ~ spl53_2 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f470,plain,
( ~ spl53_1
| spl53_2 ),
inference(avatar_split_clause,[],[f430,f468,f464]) ).
fof(f472,definition,
( spl53_3
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f475,plain,
( spl53_3
| spl53_2 ),
inference(avatar_split_clause,[],[f429,f468,f472]) ).
fof(f477,definition,
( spl53_4
<=> sK50 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f479,plain,
( sK50 = app(sK52,cons(sK51,nil))
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f481,definition,
( spl53_5
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f484,plain,
( spl53_4
| ~ spl53_5 ),
inference(avatar_split_clause,[],[f412,f481,f477]) ).
fof(f486,definition,
( spl53_6
<=> sK49 = app(cons(sK51,nil),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f488,plain,
( sK49 = app(cons(sK51,nil),sK52)
| ~ spl53_6 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f489,plain,
( spl53_6
| ~ spl53_5 ),
inference(avatar_split_clause,[],[f413,f481,f486]) ).
fof(f491,definition,
( spl53_7
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_7])],[avatar_definition]) ).
fof(f493,plain,
( ssList(sK52)
| ~ spl53_7 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f494,plain,
( spl53_7
| ~ spl53_5 ),
inference(avatar_split_clause,[],[f414,f481,f491]) ).
fof(f496,definition,
( spl53_8
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_8])],[avatar_definition]) ).
fof(f498,plain,
( ssItem(sK51)
| ~ spl53_8 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f499,plain,
( spl53_8
| ~ spl53_5 ),
inference(avatar_split_clause,[],[f415,f481,f496]) ).
fof(f500,plain,
( ~ spl53_1
| spl53_5 ),
inference(avatar_split_clause,[],[f428,f481,f464]) ).
fof(f501,plain,
( spl53_3
| spl53_5 ),
inference(avatar_split_clause,[],[f427,f481,f472]) ).
fof(f502,plain,
( spl53_1
| ~ spl53_3 ),
inference(avatar_split_clause,[],[f418,f472,f464]) ).
fof(f535,plain,
( ! [X0] :
( ~ ssList(X0)
| sK50 != app(X0,cons(sK51,nil))
| sK49 != app(cons(sK51,nil),X0) )
| ~ spl53_2
| ~ spl53_8 ),
inference(resolution,[],[f469,f498]) ).
fof(f538,plain,
( sK50 != app(sK52,cons(sK51,nil))
| sK49 != app(cons(sK51,nil),sK52)
| ~ spl53_2
| ~ spl53_7
| ~ spl53_8 ),
inference(resolution,[],[f535,f493]) ).
fof(f539,plain,
( sK49 != app(cons(sK51,nil),sK52)
| ~ spl53_2
| ~ spl53_4
| ~ spl53_7
| ~ spl53_8 ),
inference(forward_subsumption_resolution,[],[f538,f479]) ).
fof(f558,plain,
( $false
| ~ spl53_2
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7
| ~ spl53_8 ),
inference(forward_subsumption_resolution,[],[f539,f488]) ).
fof(f559,plain,
( ~ spl53_2
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7
| ~ spl53_8 ),
inference(avatar_contradiction_clause,[],[f558]) ).
cnf(s1,plain,
( ~ spl53_1
| spl53_2 ),
inference(sat_conversion,[],[f470]) ).
cnf(s2,plain,
( spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f475]) ).
cnf(s3,plain,
( spl53_4
| ~ spl53_5 ),
inference(sat_conversion,[],[f484]) ).
cnf(s4,plain,
( ~ spl53_5
| spl53_6 ),
inference(sat_conversion,[],[f489]) ).
cnf(s5,plain,
( ~ spl53_5
| spl53_7 ),
inference(sat_conversion,[],[f494]) ).
cnf(s6,plain,
( ~ spl53_5
| spl53_8 ),
inference(sat_conversion,[],[f499]) ).
cnf(s7,plain,
( ~ spl53_1
| spl53_5 ),
inference(sat_conversion,[],[f500]) ).
cnf(s8,plain,
( spl53_3
| spl53_5 ),
inference(sat_conversion,[],[f501]) ).
cnf(s9,plain,
( spl53_1
| ~ spl53_3 ),
inference(sat_conversion,[],[f502]) ).
cnf(s20,plain,
( ~ spl53_2
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7
| ~ spl53_8 ),
inference(sat_conversion,[],[f559]) ).
cnf(s24,plain,
spl53_3,
inference(rat,[],[s20,s3,s4,s5,s6,s2,s8]) ).
cnf(s25,plain,
spl53_1,
inference(rat,[],[s9,s24]) ).
cnf(s26,plain,
spl53_5,
inference(rat,[],[s7,s25]) ).
cnf(s27,plain,
spl53_2,
inference(rat,[],[s1,s25]) ).
cnf(s28,plain,
spl53_8,
inference(rat,[],[s6,s26]) ).
cnf(s29,plain,
spl53_7,
inference(rat,[],[s5,s26]) ).
cnf(s30,plain,
spl53_6,
inference(rat,[],[s4,s26]) ).
cnf(s31,plain,
spl53_4,
inference(rat,[],[s3,s26]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s20,s28,s29,s30,s31,s27]) ).
fof(f560,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:06:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.27 % (44700)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (44709)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=106757635:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (44706)% WARNING: option uhcvi not known.
% 0.18/0.27 % (44709) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-44700-44709"...
% 0.18/0.27 % (44709)...printing done.
% 0.18/0.27 % (44705)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2951382344_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (44706)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2587674256:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (44707)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3629663323:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (44708)dis+10_1_sil=32000:sp=arity:random_seed=3510127730:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (44710)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3430081875:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (44709)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (44709)------------------------------
% 0.18/0.27 % (44709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (44709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (44709)CaDiCaL version: 2.1.3
% 0.18/0.27 % (44709)Termination reason: Refutation
% 0.18/0.27 % (44709)Time elapsed: 0.007 s
% 0.18/0.27 % (44709)Peak memory usage: 13 MB
% 0.18/0.27 % (44709)Instructions burned: 19 (million)
% 0.18/0.27 % (44700)Success in time 0.043 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------